Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawall. The Texas plant has 50 employees; the Hawall plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. Round your answers to four decimal places.. a. What is the probability that none of the employees in the sample work at the plant in Hawaii? b. What is the probability that 1 of the employees in the sample works at the plant in Hawail? c. What is the probability that 2 or more of the employees in the sample work at the plant in Hawaii? d. What is the probability that 9 of the employees in the sample work at the plant in Texas?
Answers
a. Probability that none of the employees in the sample work at the plant in Hawaii: 0.0385
b. Probability that 1 of the employees in the sample works at the plant in Hawaii: 0.3823
c. Probability that 2 or more of the employees in the sample work at the plant in Hawaii: 0.5792
d. Probability that 9 of the employees in the sample work at the plant in Texas: 0.2707
a. To find the probability that none of the employees in the sample work at the plant in Hawaii, we need to calculate the probability of selecting all employees from the Texas plant.
The probability of selecting an employee from the Texas plant is (number of employees in Texas plant)/(total number of employees) = 50/70 = 0.7143.
Since we are sampling without replacement, the probability of selecting all employees from the Texas plant is:
P(All employees from Texas) = \((0.7143)^{10}\) ≈ 0.0385.
Therefore, the probability that none of the employees in the sample work at the plant in Hawaii is approximately 0.0385.
b. To find the probability that 1 of the employees in the sample works at the plant in Hawaii, we need to calculate the probability of selecting exactly 1 employee from the Hawaii plant.
The probability of selecting an employee from the Hawaii plant is (number of employees in Hawaii plant)/(total number of employees) = 20/70 = 0.2857.
The probability of selecting exactly 1 employee from the Hawaii plant is given by the binomial probability formula:
P(1 employee from Hawaii) = \(C(10, 1) * (0.2857)^1 * (1 - 0.2857)^{10-1}\) ≈ 0.3823.
Therefore, the probability that 1 of the employees in the sample works at the plant in Hawaii is approximately 0.3823.
c. To find the probability that 2 or more of the employees in the sample work at the plant in Hawaii, we need to calculate the complementary probability of selecting 0 or 1 employee from the Hawaii plant.
P(2 or more employees from Hawaii) = 1 - P(0 employees from Hawaii) - P(1 employee from Hawaii)
P(2 or more employees from Hawaii) = 1 - 0.0385 - 0.3823 ≈ 0.5792.
Therefore, the probability that 2 or more of the employees in the sample work at the plant in Hawaii is approximately 0.5792.
d. To find the probability that 9 of the employees in the sample work at the plant in Texas, we need to calculate the probability of selecting exactly 9 employees from the Texas plant.
The probability of selecting an employee from the Texas plant is 0.7143 (as calculated in part a).
The probability of selecting exactly 9 employees from the Texas plant is given by the binomial probability formula:
P(9 employees from Texas) = \(C(10, 9) * (0.7143)^9 * (1 - 0.7143)^{10-9}\) ≈ 0.2707.
Therefore, the probability that 9 of the employees in the sample work at the plant in Texas is approximately 0.2707.
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Related Questions
There are black and white counters in a bag in the ratio 20:17
There are 54
more black counters than white counters.
How many black counters are there?
Answers
There are 360 black counters and 306 white counter in 20:17 ratio.
Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:
B/W = 20/17
We also know that there are 54 more black counters than white counters, which means that:
B = W + 54
We can use substitution to solve for B. Substituting the second equation into the first equation, we get:
(W + 54)/W = 20/17
Cross-multiplying, we get:
17(W + 54) = 20W
Expanding the left side, we get:
17W + 918 = 20W
Subtracting 17W from both sides, we get:
918 = 3W
Dividing both sides by 3, we get:
W = 306
Now we can use the second equation to find B:
B = W + 54 = 306 + 54 = 360
Therefore, there are 360 black counters in the bag.
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50 POINTS !!!!
HELP ME PLZZ I NEED HELP WITH THIS!!
Answers
твоја симпатијатвоја симпатијатвоја симпатијатвоја симпатијатвоја симпатијатвоја симпатија
Answer: 5.50
Step-by-step explanation:
1.50 + 1.00 = 2.50 . 8.00 - 2.50 = 5.50
In the triangle below the long leg is 12 in Find the length of the hypotenuse using shortcuts. find the length and use the swamps calculator use square root of 3=1.7 and round the final length to the nearest tenth and enter the number only?
Answers
The length of the hypotenuse is approximately 14.1 inches (rounded to the nearest tenth).
In the given triangle, the long leg is 12 inches. Since the triangle is a 30-60-90 triangle, the ratio of the sides is 1:√3:2.
The long leg corresponds to the side with the ratio of √3, so to find the hypotenuse, you can use the proportion:
Long leg / Hypotenuse = √3 / 2
Substitute the given values:
12 / Hypotenuse = 1.7 / 2
To find the hypotenuse, cross-multiply and divide:
Hypotenuse = (12 * 2) / 1.7 ≈ 14.1
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Suppose we want to compute x ≡ a^b (mod pq) for primes p and q, utilizing the Chinese Remainder Theorem and Fermat's Little Theorem. Select the true statements. The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations. Fermat's Little Theorem allows us to conclude that ap^−1≡1(mod p) for any integer a and any prime p. By CRT,x=(a^b mod p) (q^−1 mod p) q + (ab mod p)(p^−1 mod q) p
By CRT,x=(a^b mod q)(q^−1 mod p) q + (a^b mod q)(p^−1 mod q) p
Ifb≥p, then a^b−p+1≡a^b (mod p)
If b ≡ c (mod p), then a^b≡a^c (mod p)
Answers
The true statements are: The Chinese Remainder Theorem guarantees a unique solution to any system of modular equations.
Fermat's Little Theorem allows us to conclude that ap^−1≡1(mod p) for any integer a and any prime p.
The first formula given in the question for computing x using CRT is also true.
Statement 3, "If b≥p, then a^b−p+1≡a^b (mod p)", is not necessarily true. Fermat's Little Theorem states that if p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p). However, this does not extend to arbitrary exponents b.
Statement 4, "If b ≡ c (mod p), then a^b≡a^c (mod p)" is true by Fermat's Little Theorem, which implies that a^(p-1) ≡ 1 (mod p), we can write b = kp + c for some integer k, then
a^b = a^(kp+c) = (a^p)^k * a^c ≡ a^c (mod p)
since a^p ≡ a^(p-1) * a ≡ 1 * a ≡ a (mod p) by Fermat's Little Theorem.
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STANDARDIZED TEST PRACTICE
12.) The model represents the equation x + 1 = 7.
Which is the first step in finding the value of x?
a.) Add counters to each side.
b) Subtract 7 counters from each side.
c.) Add 7 counters to each side.
d.) Subtract 4 counters from each side.
Answers
Answer:
x+1=7 (x=6)
Step-by-step explanation:
you add to the right side of the equation, and you get 6. hope this helps!
2. Given that the linear system Ax=b has a particular solution p. Show that for every solution y of Ax=b, there is a solution v of the homogeneous linear system Ax=0 such that y=p+v. Hint: Consider y−p.
Answers
This proves that for every solution y of Ax = b, there is a solution v of the homogeneous linear system Ax = 0 such that y = p + v.
Given that the linear system Ax = b has a particular solution p.
We are supposed to show that for every solution y of Ax = b, there is a solution v of the homogeneous linear system Ax = 0 such that y = p + v.
Hint: Consider y - p.
To prove this, we can consider the difference between the two solutions y and p and take that as our solution v of Ax = 0.
Since p is a solution to Ax = b,
it follows that Ap = b.
Since y is also a solution to Ax = b,
it follows that Ay = b.
We can subtract the two equations to get:
Ay - Ap = 0 which gives us:
A(y - p) = 0
So, the solution to Ax = 0 is y - p,
which means that there exists some vector v such that Av = 0 and y - p = v.
Therefore, we have y = p + v where v is a solution of Ax = 0.
Hence, this proves that for every solution y of Ax = b, there is a solution v of the homogeneous linear system Ax = 0 such that y = p + v.
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Let the long-run profit function for a representative firm is given by π i
=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.
Answers
(a) The firm's output supply function is given by q = (p + 199) / 2.
(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.
(c) Each firm sells 70 computers in the long run.
To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:(39 - 0.009q) = (2q - 2) / q
Simplifying the equation, we find:
q = (p + 199) / 2
This represents the firm's output supply function.
To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:p = 39 - 0.009((p + 199) / 2)
Simplifying and solving for p, we get:
p ≈ $32.56
Substituting this price back into the output supply function, we find:
q = (32.56 + 199) / 2 ≈ 115.78
Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:
Number of firms = q / 70 ≈ 10
Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:70 * 10 = 700
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![[tex]\huge\bold\red{{HELP}}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/fMRuWtHXHMb68jEewtXUZJ65FnvdT5uP.jpeg)
Answers
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
The linear term in the given function is :
\(5x\)\(\mathrm{✌TeeNForeveR✌}\)
Answer:
The linear term is \(\sf5x\)
Therefore, the linear term of the given Quadratic function is \(\sf5x\).Hope it helps you!
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PLEASE HELP I WILL MARK BRAINLIST!!!!!! ITS A GEOMETRY QUESTION !!! Consider a right triangle ABC, where angle C is the right angle. If the side opposite of angle A is 15 cm and the hypotenuse is 17 cm, then what should represent the measure of angle A?
Answers
Step-by-step explanation:
\( \sin(a) = \frac{15}{17} \\ a = {sin}^{ - 1} ( \frac{15}{17} )\)
HOPE THIS HELPS!!!
Answer:
\(\sin^{-1}\left({\dfrac{15}{17}}\right)\)
Step-by-step explanation:
The law of sines for a triangle states that the ratio of the side of a triangle to its opposite angle is the same for all sides and all opposite angles
Look at the attached figure.
The side opposite angle C is 17 cm so 17/sinC is the ratio. C is 90° and sin90° = 1 so this ratio is just 1/1 = 17
The side opposite angle A has 15 in length
So 15/sinA is the ratio
Using the law of sines,
15/sinA = 17
\(\sin(A) = \dfrac{15}{17}\\\\A = \sin^{-1}\left({\dfrac{15}{17}}\right)\)
the question is in the image
Answers
For the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
As given,
Graph of parabola shows it open down parabola.
Vertex is the highest point on the graph of parabola.
it is known as the maximum value.
Let (h, k) be the vertex of the given parabola.
From the graph value of the vertex is equal to :
(h ,k)=(1, -4)
h represents the x-coordinate.
k represents the y-coordinate.
y-coordinate represents the maximum value of the parabola.
y =-4 is the maximum value.
Therefore, for the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
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2. Bucky walked 85 feet. His friend in Canada wanted to
know how many meters he walked.
Given that 1 foot = .3048 meter, how many meters
did Bucky walk?
Answers
Using metric system , we have cοme tο find that Bucky walked 25.908 meter.
What is metric system?Metric system is a prοcess οf measuring things. It is used tο measure length, vοlume , weight , capacity etc. In metric system οne unit can be cοnverted intο anοther unit.
Given that Bucky walked 85 feet. His friend in Canada wanted tο
knοw hοw many meters he walked.
Given that 1 fοοt = .3048 meter
Tο cοnvert 85 feet tο meter we are gοing tο use the metric system.
1 fοοt = 0.3048 meter
85 fοοt = 85 × 0.3048 meter [ Since in metric system , tο cοvert a unit frοm anοther unit either have tο multiply οr have tο divide the unit]
By multiplying we get 25.908 meter.
Hence, Bucky walked 25.908 meter.
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solve in 25 mins I will give thumb up
8. Consider a 1-year semi-annually paid interest rate swap, the notional is \( £ 1,000,000 \), the swap rate is \( 3.0 \% \), the flouting rate is \( 6 \mathrm{M} \) LIBOR \( +1 \% \). On the market,
Answers
In a 1-year semi-annually paid interest rate swap, with a notional amount of £1,000,000, the swap rate is 3.0%. The floating rate is based on the 6-month LIBOR plus 1%. The market rate refers to the prevailing interest rate for the specified time period.
An interest rate swap involves the exchange of cash flows between two parties based on different interest rate benchmarks. In this case, the swap has a 1-year maturity and payments are made semi-annually.
The fixed rate, also known as the swap rate, is determined at the beginning of the swap agreement and remains fixed throughout the swap's duration. In this scenario, the swap rate is 3.0%.
The floating rate is determined by a reference rate plus a spread. The reference rate used here is the 6-month LIBOR (London Interbank Offered Rate), which is a widely used benchmark for short-term interest rates. The floating rate in this swap is the 6-month LIBOR plus 1%.
The market rate refers to the prevailing interest rate for the specified time period. It represents the current market conditions and influences the pricing and valuation of the interest rate swap.
To fully analyze the swap and its implications, further calculations and considerations, such as the present value of cash flows and potential valuation changes based on market rate movements, would be necessary.
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The marked price of a book is $1 100. During a sale a 30% discount given. Calculate the sale price.
Answers
Answer:
770
Step-by-step explanation:
1 100 - 30℅ will give you 770 as your answer
An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the stay, y, for different numbers of nights, x, for the two different resorts.
Which statement correctly compares the nightly rates at Stargazer Suites and Retro Retreat?
The nightly rate at Stargazer Suites is $15 more than the nightly rate at Retro Retreat.
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
The nightly rate at Retro Retreat is $30 more than the nightly rate at Stargazer Suites.
The nightly rate at Retro Retreat is $80 more than the nightly rate at Stargazer Suites.
The nightly rate at each resort is the same.
Answers
Answer:
to confusing
Step-by-step explanation:
Answer:
The nightly rate at Stargazer Suites is $25 more than the nightly rate at Retro Retreat.
Step-by-step explanation:
our school's girls volleyball team has $14$ players, including a set of $3$ triplets: alicia, amanda, and anna. in how many ways can we choose $6$ starters with no restrictions? (the triplets are treated as distinguishable.)
Answers
There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.
= C(3,2) = 3! / ( 2! x 1! ) = 3
To select the final 4 starters out of the 11 players ,
= C(11,4) = 11! / (4!7!)
= 330
There are a total of 6 ways to select starters.
= 3*330 = 990
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.
The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
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use the elimination method to solve for the general solution to the system
x'= x-y
y''= -2x'+e^t
Answers
The general solution to the given system of differential equations is:
x(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)
y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)
where c1, c2, and c3 are constants determined by initial conditions or specific constraints.
To solve the system using the elimination method, we need to eliminate one variable at a time. Let's start by eliminating x.
x' = x - y ...........(1)
y'' = -2x' + e^t ...........(2)
First, differentiate equation (1) with respect to t to get:
x'' = x' - y' ...........(3)
Now substitute the value of x' from equation (3) into equation (2):
y'' = -2(x' - y) + e^t
y'' = -2x' + 2y + e^t ...........(4)
To eliminate x', we subtract equation (4) from equation (2):
y'' - y' = e^t ...........(5)
Next, differentiate equation (5) with respect to t:
y''' - y'' = e^t ...........(6)
Now we have two equations:
y'' - y' = e^t ...........(5)
y''' - y'' = e^t ...........(6)
To solve these equations, we can solve equation (6) for y'' and substitute it into equation (5):
(y''' - e^t) - (y'' - y') = e^t
y''' - y'' + y' - e^t = e^t
y''' - y'' + y' = 2e^t ...........(7)
Equation (7) is a third-order linear homogeneous differential equation for y.
To find the general solution to equation (7), we solve its characteristic equation:
r^3 - r^2 + r = 0
Factoring out an r, we get:
r(r^2 - r + 1) = 0
This equation has one real root r = 0 and two complex roots r = (1 ± √3i)/2.
Therefore, the general solution for y is:
y(t) = c1 + c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)
Now, we can substitute the general solution for y into equation (5) to solve for x:
y'' - y' = e^t
(c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2))' - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t
Differentiating and simplifying, we get:
(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - (c2e^tcos((√3t)/2) + c3e^tsin((√3t)/2)) = e^t
Simplifying further, we get:
(-c2e^t(√3/2)sin((√3t)/2) + c3e^t(√3/2)cos((√3t)/2)) - c2e^tcos((√3t)/2) - c3e^tsin((√3t)/2) = e^t
Now, equating the coefficients of e^t and the trigonometric terms, we can solve for c1, c2, and c3.
This completes the solution process using the elimination method for the given system of differential equations.
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28. Given M₁ = 35, M₂ = 45, and SM1-M2= 6.00, what is the value of t? -2.92 -1.67 O-3.81 2.75
Answers
The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
Given, M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.
To calculate the t-value,
the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
The circumference of a circular lawn is 110 feet. If you double the radius, what will the new circumference be?
Answers
Answer:
220
Step-by-step explanation:
The new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have:
The circumference of a circular lawn is 110 feet.
2πr = 110
r = 55/π
Double the radius:
R = 2r= 110/π
New circumference = 2πR = 2π(110/π) = 220 feet
Thus, the new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.
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ok Im pretty sure this photo is clearer
Answers
Answer:D or C
Step-by-step explanation:
Solve −18=6+6x .
x = __
Answers
Answer:
x = -4
Step-by-step explanation:
-18 = 6+6x
-18 -6 = 6x
-24 = 6x
-24/6 = x
x = -4
Checking Part:
-18 = 6 + 6x
-18 = 6 + 6(-4)
-18 = 6 -24
-18 = -18
Answer:
-4
Step-by-step explanation:
Subtract 6 to get X by itself and that leaver you with - 24=6x now divide by 6 to get x=-4
Hope this helps
Plz help Can you plot the data !
9b) write the equation of your best fitting line.
9c)use your to determine how well you would do if for 4 hours
Answers
Answer:
9b y= 15.109t + 56.4
9c 116.836 in 4 hours
Step-by-step explanation:
I used a regression calculator for the first one.
I multiplied 15.109 and 4 because t is the time.
add 56.4
look at picture and solve
Answers
Answer:
79°
Step-by-step explanation:
PQO is straight angle with measure of 180°
the given angles' sum makes 101° and we need 79 to complete it to 180° therefore the angle STQ = 79°
if vector is added to vector , the result is . if is subtracted from , the result is . what is the direction of (to the nearest degree)?
Answers
The direction of vector D is perpendicular to vector A, and it makes an angle of 90 degrees with vector A.
We are given that:
vector A + vector B = vector C
vector A - vector B = vector D
To find the direction of vector C,
we can use the fact that the tangent of the angle between vector A and vector C is equal to the ratio of their magnitudes.
That is:
tan(theta) = |vector C| / |vector A|
where theta is the angle between vector A and vector C.
Similarly, to find the direction of vector D,
we can use the fact that the tangent of the angle between vector A and vector D is equal to the ratio of their magnitudes.
That is:
tan(phi) = |vector D| / |vector A|
where phi is the angle between vector A and vector D.
We want to find the angle between vector A and vector D, which is equal to the supplement of the angle between vector A and vector C.
That is:
theta + phi = 180 degrees
Rearranging, we get:
phi = 180 degrees - theta
Substituting the equations for theta and phi, we get:
tan(180 degrees - phi) = |vector D| / |vector A| = tan(phi)
Simplifying, we get:
tan(180 degrees - phi) = tan(phi)
Using the identity tan(180 degrees - theta) = -tan(theta), we can rewrite this as:
-tan(phi) = tan(phi)
Solving for phi, we get:
2*phi = 180 degrees
phi = 90 degrees
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Complete question may be:
If, vector A + vector B = vector Cvector A - vector B = vector D, then find the direction of vector D is perpendicular to vector A?
a report says that the average amount of time a 10-year-old american child spends playing outdoors per day is between 20.08 and 24.78 minutes. what is the margin of error in this report?
Answers
The margin of error in the report is 2.35 minutes.
The margin of error is a measure of the amount of uncertainty or error associated with a survey or study's results. It represents the range within which the true value of a population parameter is likely to lie, given the sample size and sampling method used. In this case, the report provides a range for the average amount of time a 10-year-old American child spends playing outdoors per day. The margin of error can be calculated as half the width of the confidence interval, which is (24.78 - 20.08)/2 = 2.35 minutes. This means that if the study were repeated many times, 95% of the time the true average time spent playing outdoors per day for 10-year-old American children would be within 2.35 minutes of the reported range.
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A restaurant offers delivery for their pizzas and includes the delivery fee in the total price of the pizzas.
One customer pays $$ to have $$ pizzas delivered.
Another customer pays $$ for $$ pizzas.
How many pizzas are delivered to a customer who pays $$?
Answers
2-simplifica
1)x²-5x-16
x+2=
2)6an²-3b²n²
b4-4ab²+4a²=
3)4x²-4xy+y²
5y-10x
4)n+1-n³-n²
n³-n-2n²+2=
5)17x³y4z6
34x7y8z10=
6)12a²b³
60a³b5x6=
Answers
1. x² - 5x - 16 can be written as (x - 8)(x + 2).
2. 6an² - 3b²n² = n²(6a - 3b²).
3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².
4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
5. 17x³y⁴z⁶ = (x²y²z³)².
6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
Let's simplify the given expressions:
Simplifying x² - 5x - 16:
To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.
Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).
Simplifying 6an² - 3b²n²:
To simplify this expression, we can factor out the common term n² from both terms:
6an² - 3b²n² = n²(6a - 3b²).
Simplifying 4x² - 4xy + y²:
This expression represents a perfect square trinomial, which can be factored as (2x - y)².
Simplifying n + 1 - n³ - n²:
Rearranging the terms, we have -n³ - n² + n + 1.
Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).
Simplifying 17x³y⁴z⁶:
To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:
17x³y⁴z⁶ = (x²y²z³)².
Simplifying 12a²b³:
To simplify this expression, we can multiply the exponents of a and b with the given expression:
12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.
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The table shows a proportional relationship.
x 15 9 21
y 5 3 7
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (15, 5).
A line passes through the point (0, 0) and continues through the point (7, 21).
A line passes through the point (0, 0) and continues through the point (5, 15).
A line passes through the point (0, 0) and continues through the point (3, 9).
PLS HELP
Answers
The statement that describes the graph of the proportional relationship is:
"A line passes through the point (0, 0) and continues through the point (15, 5)."
How the proportional relationship would look like?We have a proportional relationship defined by the following table:
x: 15, 8, 21
y: 5, 3, 7
Remember that a general proportional relationship is given by the formula:
y = k*x
Where k is the constant of proportionality.
If we take x = 0, we always get:
y = k*0
y = 0
So the line always passes through the point (0, 0).
And by using the information on the table, we also know that the line passes through (15, 5), (9,3) and (21, 7).
Then the correct option is:
"A line passes through the point (0, 0) and continues through the point (15, 5)."
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Please do number 2 QUICK
Answers
Answer:
25
Step-by-step explanation:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
Answer:
25
Step-by-step explanation:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Which month could be used as a counterexample for the argument All months have at least 30 days.?
A.) February
B.) September
C.) April
D.) July
Answers
Answer:
february
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